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Information 2018, 9(6), 137; https://doi.org/10.3390/info9060137

A Novel Method for Determining the Attribute Weights in the Multiple Attribute Decision-Making with Neutrosophic Information through Maximizing the Generalized Single-Valued Neutrosophic Deviation

1
School of Mathematics and Statistics, Hubei Engineering University, Xiaogan 432000, China
2
School of Economics and Management, Hubei Engineering University, Xiaogan 432000, China
*
Author to whom correspondence should be addressed.
Received: 19 April 2018 / Revised: 28 May 2018 / Accepted: 1 June 2018 / Published: 7 June 2018
(This article belongs to the Section Information Theory and Methodology)
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Abstract

The purpose of this paper is to investigate the weights determination in the multiple attribute decision-making (MADM) with the single valued neutrosophic information. We first introduce a generalized single-valued neutrosophic deviation measure for a group of single valued neutrosophic sets (SVNSs), and then present a novel and simple nonlinear optimization model to determine the attribute weights by maximizing the total deviation of all attribute values, whether the attribute weights are partly known or completely unknown. Compared with the existing method based on the deviation measure, the presented approach does not normalize the optimal solution and is easier to integrate the subjective and objective information about attribute weights in the neutrosophic MADM problems. Moreover, the proposed nonlinear optimization model is solved to obtain an exact and straightforward formula for determining the attribute weights if the attribute weights are completely unknown. After the weights are obtained, the neutrosophic information of each alternative is aggregated by using the single valued neutrosophic weighted average (SVNWA) operator. In what follows, all alternatives are ranked and the most preferred one(s) is easily selected according to the score function and accuracy function. Finally, an example in literature is examined to verify the effectiveness and application of the developed approach. The example is also used to demonstrate the rationality for overcoming some drawbacks of the existing approach according to the maximizing deviation method. View Full-Text
Keywords: single valued neutrosophic set (SVNS); generalized single-valued neutrosophic deviation measure; multiple attribute decision-making; attribute weights single valued neutrosophic set (SVNS); generalized single-valued neutrosophic deviation measure; multiple attribute decision-making; attribute weights
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Xiong, W.; Cheng, J. A Novel Method for Determining the Attribute Weights in the Multiple Attribute Decision-Making with Neutrosophic Information through Maximizing the Generalized Single-Valued Neutrosophic Deviation. Information 2018, 9, 137.

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